MHT CET · Physics · Thermal Properties of Matter
For a perfectly black body, the graph is plotted between the frequency of radiation with maximum intensity \(\left(v_{\mathrm{m}}\right)\) and the absolute temperature ' \(\mathrm{T}\) '. Out of the following which is the correct graph?
- A C
- B A
- C D
- D B
Answer & Solution
Correct Answer
(D) B
Step-by-step Solution
Detailed explanation
According to Wein's displacement law \(\lambda_{\mathrm{m}} \mathrm{T}=\mathrm{b}=\) Wein constant
If \(v_m\) is the frequency corresponding to wavelength \(\lambda_m\), then
\(\left(\frac{\mathrm{c}}{\mathrm{u}_{\mathrm{m}}}\right) \mathrm{T}=\mathrm{b}\)
or \(\mathrm{u}_{\mathrm{m}}=\frac{\mathrm{c}}{\mathrm{b}} \mathrm{T}\), i.e.,
\(\mathrm{u}_{\mathrm{m}} \propto \mathrm{T}\)
\(\therefore v_{\mathrm{m}}\) graph is linear w.r.t. temperature and the straingth line shown by line \(\mathrm{B}\). Thus, option (D) is true.
If \(v_m\) is the frequency corresponding to wavelength \(\lambda_m\), then
\(\left(\frac{\mathrm{c}}{\mathrm{u}_{\mathrm{m}}}\right) \mathrm{T}=\mathrm{b}\)
or \(\mathrm{u}_{\mathrm{m}}=\frac{\mathrm{c}}{\mathrm{b}} \mathrm{T}\), i.e.,
\(\mathrm{u}_{\mathrm{m}} \propto \mathrm{T}\)
\(\therefore v_{\mathrm{m}}\) graph is linear w.r.t. temperature and the straingth line shown by line \(\mathrm{B}\). Thus, option (D) is true.
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